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Номер 163, страница 52 - гдз по алгебре 9 класс учебник Солтан, Солтан
Авторы: Солтан Г. Н., Солтан А. Е., Жумадилова А. Ж.
Тип: Учебник
Издательство: Кокшетау
Год издания: 2019 - 2026
ISBN: 978-601-317-424-2
Рекомендовано Министерством образования и науки Республики Казахстан
Популярные ГДЗ в 9 классе
I. Уравнения, неравенства с двумя переменными и их системы. 5. Системы неравенств с двумя переменными - номер 163, страница 52.
App\Models\Task {#1030 // resources/views/models/task/default.blade.php #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1107862 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "52" "field_page_end" => null "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik/1-163" "field_display_title" => "163" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037 #items: array:1 [ 0 => App\Models\Term {#1036 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #original: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1071 #items: array:1 [ 0 => App\Models\Branch {#1034 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1107639 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "I. Уравнения, неравенства с двумя переменными и их системы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "18" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1038 #items: array:1 [ 0 => App\Models\Book {#1040 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 4298 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1041 #items: array:1 [ 0 => App\Models\Term {#1042 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ …10] #original: array:10 [ …10] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1043 #items: array:1 [ 0 => App\Models\Term {#1044 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1045 #items: array:1 [ 0 => App\Models\Term {#1046 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1047 #items: array:3 [ 0 => App\Models\Term {#1048 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ …12] #original: array:12 [ …12] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 1 => App\Models\Term {#1049 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ …12] #original: array:12 [ …12] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 2 => App\Models\Term {#1050 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ …12] #original: array:12 [ …12] …16 } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1051 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1052 #items: array:1 [ 0 => App\Models\Term {#1053 …30} ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1054 #items: array:1 [ 0 => App\Models\Term {#1055 …30} ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1056 #items: array:1 [ 0 => App\Models\Term {#1057 …30} ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1058 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1059 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1060 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1061 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1062 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1063 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся 9 класса общеобразовательных школ" "field_allowed" => "Рекомендовано Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => "4" "field_default_folder" => "/algebra_09/soltan-u19/" "field_isbn" => "978-601-317-424-2" "field_cover" => array:1 [ 0 => "/media/algebra_09/soltan-u19/covers/cover1.webp?ts=1752140452" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/algebra_09/soltan-u19/covers/cover1.webp?ts=1752140452" "alt" => "" "width" => "1940" "height" => "2895" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1064 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1065 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1066 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1067 #items: [] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 380 "subject" => 542 "class_subject" => 386 ] ] #original: array:50 [ "id" => 4298 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1041} "field_class" => Illuminate\Database\Eloquent\Collection {#1043} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1045} "field_author" => Illuminate\Database\Eloquent\Collection {#1047} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1051} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1052} "field_country" => Illuminate\Database\Eloquent\Collection {#1054} "field_city" => Illuminate\Database\Eloquent\Collection {#1056} "field_series" => Illuminate\Database\Eloquent\Collection {#1058} "field_umk" => Illuminate\Database\Eloquent\Collection {#1059} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1060} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1061} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1062} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1063} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся 9 класса общеобразовательных школ" "field_allowed" => "Рекомендовано Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => "4" "field_default_folder" => "/algebra_09/soltan-u19/" "field_isbn" => "978-601-317-424-2" "field_cover" => array:1 [ 0 => "/media/algebra_09/soltan-u19/covers/cover1.webp?ts=1752140452" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/algebra_09/soltan-u19/covers/cover1.webp?ts=1752140452" "alt" => "" "width" => "1940" "height" => "2895" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1064} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1065} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1066} "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1067} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 380 "subject" => 542 "class_subject" => 386 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1068 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1107639 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "I. Уравнения, неравенства с двумя переменными и их системы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039} "field_page_start" => "18" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1038} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1068} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1104 #items: array:2 [ 0 => App\Models\Branch {#1112 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1107639 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "I. Уравнения, неравенства с двумя переменными и их системы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1113 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "18" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1144 #items: array:1 [ 0 => App\Models\Book {#1114 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 4298 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1116 #items: array:1 [ 0 => App\Models\Term {#1115 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6471 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Алгебра" "field_abbreviated_name" => null "field_cases" => array:6 [ "field_accusative_case" => "алгебру" "field_creative_case" => "алгеброй" "field_dative_case" => "алгебре" "field_genitive_case" => "алгебры" "field_nominative_case" => "алгебра" "field_prepositional_case" => "алгебре" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "algebra" ] #original: array:10 [ "id" => 6471 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Алгебра" "field_abbreviated_name" => null "field_cases" => array:6 [ "field_accusative_case" => "алгебру" "field_creative_case" => "алгеброй" "field_dative_case" => "алгебре" "field_genitive_case" => "алгебры" "field_nominative_case" => "алгебра" "field_prepositional_case" => "алгебре" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "algebra" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1117 #items: array:1 [ 0 => App\Models\Term {#1118 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ "field_accusative_case" => "девятый" "field_creative_case" => "девятым" "field_dative_case" => "девятому" "field_genitive_case" => "девятого" "field_nominative_case" => "девятый" "field_prepositional_case" => "девятом" ] "field_translit" => "devjatyj" ] #original: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ "field_accusative_case" => "девятый" "field_creative_case" => "девятым" "field_dative_case" => "девятому" "field_genitive_case" => "девятого" "field_nominative_case" => "девятый" "field_prepositional_case" => "девятом" ] "field_translit" => "devjatyj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1119 #items: array:1 [ 0 => App\Models\Term {#1120 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 7002 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кокшетау" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "Kokshetau" ] #original: array:6 [ "id" => 7002 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кокшетау" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "Kokshetau" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1121 #items: array:3 [ 0 => App\Models\Term {#1122 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 7003 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Солтан" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Генадий" "field_patronymic" => "Николаевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 7003 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Солтан" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Генадий" "field_patronymic" => "Николаевич" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Term {#1123 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 7004 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Солтан" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Алла" "field_patronymic" => "Евгеньевна" "field_surname_rp" => null ] #original: array:12 [ "id" => 7004 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Солтан" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Алла" "field_patronymic" => "Евгеньевна" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Term {#1124 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 7005 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Жумадилова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Аманбала" "field_patronymic" => "Жумадиловна" "field_surname_rp" => null ] #original: array:12 [ "id" => 7005 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Жумадилова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Аманбала" "field_patronymic" => "Жумадиловна" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1125 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1126 #items: array:1 [ 0 => App\Models\Term {#1127 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "учебник" "field_creative_case" => "учебником" "field_dative_case" => "учебнику" "field_genitive_case" => "учебника" "field_nominative_case" => "учебник" "field_prepositional_case" => "учебнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #original: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "учебник" "field_creative_case" => "учебником" "field_dative_case" => "учебнику" "field_genitive_case" => "учебника" "field_nominative_case" => "учебник" "field_prepositional_case" => "учебнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1128 #items: array:1 [ 0 => App\Models\Term {#1129 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 6994 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Казахстан" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "kazakhstan" ] #original: array:6 [ "id" => 6994 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Казахстан" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "kazakhstan" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1130 #items: array:1 [ 0 => App\Models\Term {#1131 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 6995 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Алматы" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "almaty" ] #original: array:6 [ "id" => 6995 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Алматы" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "almaty" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1132 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1133 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1134 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1135 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1136 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1137 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся 9 класса общеобразовательных школ" "field_allowed" => "Рекомендовано Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => "4" "field_default_folder" => "/algebra_09/soltan-u19/" "field_isbn" => "978-601-317-424-2" "field_cover" => array:1 [ 0 => "/media/algebra_09/soltan-u19/covers/cover1.webp?ts=1752140452" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/algebra_09/soltan-u19/covers/cover1.webp?ts=1752140452" "alt" => "" "width" => "1940" "height" => "2895" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1138 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1139 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1140 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1141 #items: [] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 380 "subject" => 542 "class_subject" => 386 ] ] #original: array:50 [ "id" => 4298 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1116} "field_class" => Illuminate\Database\Eloquent\Collection {#1117} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1119} "field_author" => Illuminate\Database\Eloquent\Collection {#1121} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1125} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1126} "field_country" => Illuminate\Database\Eloquent\Collection {#1128} "field_city" => Illuminate\Database\Eloquent\Collection {#1130} "field_series" => Illuminate\Database\Eloquent\Collection {#1132} "field_umk" => Illuminate\Database\Eloquent\Collection {#1133} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1134} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1135} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1136} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1137} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся 9 класса общеобразовательных школ" "field_allowed" => "Рекомендовано Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1291" "field_priority" => "4" "field_default_folder" => "/algebra_09/soltan-u19/" "field_isbn" => "978-601-317-424-2" "field_cover" => array:1 [ 0 => "/media/algebra_09/soltan-u19/covers/cover1.webp?ts=1752140452" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/algebra_09/soltan-u19/covers/cover1.webp?ts=1752140452" "alt" => "" "width" => "1940" "height" => "2895" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1138} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1139} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1140} "field_url" => "/9-klass/algebra/kokshetau-soltan-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1141} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 380 "subject" => 542 "class_subject" => 386 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1142 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1107639 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "I. Уравнения, неравенства с двумя переменными и их системы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1113} "field_page_start" => "18" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1144} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1142} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Branch {#1143 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1107644 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "5. Системы неравенств с двумя переменными" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1145 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "46" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1146 #items: array:1 [ 0 => App\Models\Book {#1114} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1147 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1107644 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "5. Системы неравенств с двумя переменными" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1145} "field_page_start" => "46" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1146} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1147} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1096 #items: array:3 [ 0 => App\Models\Element {#1085 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 1276518 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1076 #items: array:1 [ 0 => App\Models\Edition {#1086 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 4953 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1080 #items: array:1 [ 0 => App\Models\Term {#1084 …30} ] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "pasha" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1083 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1082 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1081 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 4953 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1080} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "pasha" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1083} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1082} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1081} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1107862" "type" => "task" ] "text" => "<p><strong>163.</strong> Постройте в координатной плоскости фигуру, координаты каждой точки которой являются решениями системы неравенств:</p><p><strong>a)</strong> $\begin{cases} x^2 + y^2 \le 16, \\ y \ge \frac{2}{x}, \end{cases}$</p><p><strong>б)</strong> $\begin{cases} x^2 + y \le 6, \\ |x| + y \ge 4; \end{cases}$</p><p><strong>в)</strong> $\begin{cases} 3x - y \ge 0, \\ x^2 + |y| \ge 4; \end{cases}$</p><p><strong>г)</strong> $\begin{cases} x^2 + (y - 1)^2 \le 16, \\ |y| + 3x \le 3. \end{cases}$</p>" "img" => array:1 [ 0 => array:5 [ "name" => "163-1.jpg" "alt" => null "width" => "1593" "height" => 552 "path" => "/media/algebra_09/soltan-u19/0-1/163-1.webp?ts=1752834218" ] ] ] #original: array:7 [ "id" => 1276518 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1076} "task" => array:2 [ "refs" => "1107862" "type" => "task" ] "text" => "<p><strong>163.</strong> Постройте в координатной плоскости фигуру, координаты каждой точки которой являются решениями системы неравенств:</p><p><strong>a)</strong> $\begin{cases} x^2 + y^2 \le 16, \\ y \ge \frac{2}{x}, \end{cases}$</p><p><strong>б)</strong> $\begin{cases} x^2 + y \le 6, \\ |x| + y \ge 4; \end{cases}$</p><p><strong>в)</strong> $\begin{cases} 3x - y \ge 0, \\ x^2 + |y| \ge 4; \end{cases}$</p><p><strong>г)</strong> $\begin{cases} x^2 + (y - 1)^2 \le 16, \\ |y| + 3x \le 3. \end{cases}$</p>" "img" => array:1 [ 0 => array:5 [ "name" => "163-1.jpg" "alt" => null "width" => "1593" "height" => 552 "path" => "/media/algebra_09/soltan-u19/0-1/163-1.webp?ts=1752834218" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Element {#1078 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1277809 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1107 #items: array:1 [ 0 => App\Models\Edition {#1079 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 4954 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1074 #items: array:1 [ 0 => App\Models\Term {#1077 …30} ] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "pasha" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1075 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1072 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1103 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 4954 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1074} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "pasha" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1075} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1072} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1103} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1107862" "type" => "task" ] "img" => array:2 [ 0 => array:5 [ "name" => "163-1.jpg" "alt" => null "width" => "1283" "height" => 1656 "path" => "/media/algebra_09/soltan-u19/1-1/163-1.webp?ts=1752830894" ] 1 => array:5 [ "name" => "163-2.jpg" "alt" => null "width" => "1285" "height" => 1516 "path" => "/media/algebra_09/soltan-u19/1-1/163-2.webp?ts=1752830894" ] ] ] #original: array:6 [ "id" => 1277809 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1107} "task" => array:2 [ "refs" => "1107862" "type" => "task" ] "img" => array:2 [ 0 => array:5 [ "name" => "163-1.jpg" "alt" => null "width" => "1283" "height" => 1656 "path" => "/media/algebra_09/soltan-u19/1-1/163-1.webp?ts=1752830894" ] 1 => array:5 [ "name" => "163-2.jpg" "alt" => null "width" => "1285" "height" => 1516 "path" => "/media/algebra_09/soltan-u19/1-1/163-2.webp?ts=1752830894" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Element {#1102 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1553764 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1152 #items: array:1 [ 0 => App\Models\Edition {#1111 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 5665 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2 (rus)" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1108 #items: array:1 [ 0 => App\Models\Term {#1105 …30} ] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1106 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1148 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1149 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 5665 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2 (rus)" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1108} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1106} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1148} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1149} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1107862" "type" => "task" ] "text" => "<p><strong>a)</strong></p><p>Рассмотрим систему неравенств $\begin{cases} x^2 + y^2 \le 16 \\ y \ge \frac{2}{x} \end{cases}$.<br>Первое неравенство, $x^2 + y^2 \le 16$, задает круг с центром в начале координат $(0, 0)$ и радиусом $R=4$, включая его границу.<br>Второе неравенство, $y \ge \frac{2}{x}$, задает множество точек, лежащих на и выше гиперболы $y = \frac{2}{x}$. Область определения этого неравенства — все $x$, кроме $x=0$. Гипербола имеет две ветви: одну в первой координатной четверти (при $x>0$) и одну в третьей (при $x<0$).<br>Искомая фигура является пересечением этих двух множеств. Это точки круга, которые одновременно удовлетворяют условию $y \ge \frac{2}{x}$. Фигура состоит из двух отдельных частей.<br>Ответ: Искомая фигура — это множество точек круга $x^2+y^2 \le 16$, которые находятся на или выше графика гиперболы $y = 2/x$. Фигура состоит из двух непересекающихся частей.</p><p><strong>б)</strong></p><p>Рассмотрим систему неравенств $\begin{cases} x^2 + y \le 6 \\ |x| + y \ge 4 \end{cases}$.<br>Перепишем систему в более удобном для построения виде: $\begin{cases} y \le 6 - x^2 \\ y \ge 4 - |x| \end{cases}$.<br>Первое неравенство, $y \le 6 - x^2$, задает область, расположенную ниже и на параболе $y = 6 - x^2$. Это парабола с ветвями, направленными вниз, и вершиной в точке $(0, 6)$.<br>Второе неравенство, $y \ge 4 - |x|$, задает область выше и на графике функции $y = 4 - |x|$. График $y = 4 - |x|$ представляет собой "уголок" с вершиной в точке $(0, 4)$ и ветвями, направленными вниз (прямые $y=4-x$ для $x \ge 0$ и $y=4+x$ для $x < 0$).<br>Искомая фигура — это область, заключенная между графиками этих двух функций. Найдем точки их пересечения, решив уравнение $6 - x^2 = 4 - |x|$.<br>- При $x \ge 0$: $6 - x^2 = 4 - x \implies x^2 - x - 2 = 0 \implies (x-2)(x+1)=0$. Так как $x \ge 0$, то $x=2$. При этом $y=2$. Точка $(2, 2)$.<br>- При $x < 0$: $6 - x^2 = 4 + x \implies x^2 + x - 2 = 0 \implies (x+2)(x-1)=0$. Так как $x < 0$, то $x=-2$. При этом $y=2$. Точка $(-2, 2)$.<br>Ответ: Искомая фигура — это область, ограниченная сверху дугой параболы $y = 6 - x^2$ и снизу ломаной $y = 4 - |x|$, концами которой являются точки пересечения $(-2, 2)$ и $(2, 2)$.</p><p><strong>в)</strong></p><p>Рассмотрим систему неравенств $\begin{cases} 3x - y \ge 0 \\ x^2 + |y| \ge 4 \end{cases}$.<br>Перепишем систему: $\begin{cases} y \le 3x \\ |y| \ge 4 - x^2 \end{cases}$.<br>Первое неравенство, $y \le 3x$, задает полуплоскость, расположенную ниже и на прямой $y = 3x$, проходящей через начало координат.<br>Второе неравенство, $x^2 + |y| \ge 4$, задает область вне фигуры, ограниченной кривой $x^2 + |y| = 4$. Раскроем модуль:<br>- При $y \ge 0$: $x^2 + y \ge 4 \implies y \ge 4 - x^2$. Это область на и выше параболы $y = 4-x^2$.<br>- При $y < 0$: $x^2 - y \ge 4 \implies y \le x^2 - 4$. Это область на и ниже параболы $y = x^2-4$.<br>Таким образом, второе неравенство описывает всю плоскость, за исключением "глазоподобной" области между параболами $y=4-x^2$ и $y=x^2-4$.<br>Искомая фигура — это пересечение полуплоскости $y \le 3x$ и области, заданной вторым неравенством.<br>Ответ: Искомая фигура — это часть полуплоскости, лежащая на или ниже прямой $y = 3x$, из которой исключена открытая область, ограниченная кривой $x^2 + |y| = 4$.</p><p><strong>г)</strong></p><p>Рассмотрим систему неравенств $\begin{cases} x^2 + (y-1)^2 \le 16 \\ |y| + 3x \le 3 \end{cases}$.<br>Первое неравенство, $x^2 + (y-1)^2 \le 16$, задает круг с центром в точке $(0, 1)$ и радиусом $R=4$, включая его границу.<br>Второе неравенство, $|y| + 3x \le 3$, или $3x \le 3 - |y|$, задает область, ограниченную справа. Раскроем модуль:<br>- При $y \ge 0$: $y + 3x \le 3 \implies y \le 3 - 3x$. Это полуплоскость ниже и на прямой $y = 3-3x$.<br>- При $y < 0$: $-y + 3x \le 3 \implies y \ge 3x - 3$. Это полуплоскость выше и на прямой $y = 3x-3$.<br>Граница $y = 3-3x$ (для $y \ge 0$) и $y=3x-3$ (для $y < 0$) образует "уголок", открывающийся влево, с вершиной в точке $(1, 0)$. Неравенство задает область внутри этого "уголка" (то есть левее его границы).<br>Искомая фигура — это пересечение круга и области, заданной вторым неравенством.<br>Ответ: Искомая фигура — это часть круга с центром в $(0, 1)$ и радиусом 4, которая находится левее или на ломаной, состоящей из лучей $y = 3 - 3x$ для $y \ge 0$ и $y = 3x - 3$ для $y < 0$.</p>" ] #original: array:6 [ "id" => 1553764 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1152} "task" => array:2 [ "refs" => "1107862" "type" => "task" ] "text" => "<p><strong>a)</strong></p><p>Рассмотрим систему неравенств $\begin{cases} x^2 + y^2 \le 16 \\ y \ge \frac{2}{x} \end{cases}$.<br>Первое неравенство, $x^2 + y^2 \le 16$, задает круг с центром в начале координат $(0, 0)$ и радиусом $R=4$, включая его границу.<br>Второе неравенство, $y \ge \frac{2}{x}$, задает множество точек, лежащих на и выше гиперболы $y = \frac{2}{x}$. Область определения этого неравенства — все $x$, кроме $x=0$. Гипербола имеет две ветви: одну в первой координатной четверти (при $x>0$) и одну в третьей (при $x<0$).<br>Искомая фигура является пересечением этих двух множеств. Это точки круга, которые одновременно удовлетворяют условию $y \ge \frac{2}{x}$. Фигура состоит из двух отдельных частей.<br>Ответ: Искомая фигура — это множество точек круга $x^2+y^2 \le 16$, которые находятся на или выше графика гиперболы $y = 2/x$. Фигура состоит из двух непересекающихся частей.</p><p><strong>б)</strong></p><p>Рассмотрим систему неравенств $\begin{cases} x^2 + y \le 6 \\ |x| + y \ge 4 \end{cases}$.<br>Перепишем систему в более удобном для построения виде: $\begin{cases} y \le 6 - x^2 \\ y \ge 4 - |x| \end{cases}$.<br>Первое неравенство, $y \le 6 - x^2$, задает область, расположенную ниже и на параболе $y = 6 - x^2$. Это парабола с ветвями, направленными вниз, и вершиной в точке $(0, 6)$.<br>Второе неравенство, $y \ge 4 - |x|$, задает область выше и на графике функции $y = 4 - |x|$. График $y = 4 - |x|$ представляет собой "уголок" с вершиной в точке $(0, 4)$ и ветвями, направленными вниз (прямые $y=4-x$ для $x \ge 0$ и $y=4+x$ для $x < 0$).<br>Искомая фигура — это область, заключенная между графиками этих двух функций. Найдем точки их пересечения, решив уравнение $6 - x^2 = 4 - |x|$.<br>- При $x \ge 0$: $6 - x^2 = 4 - x \implies x^2 - x - 2 = 0 \implies (x-2)(x+1)=0$. Так как $x \ge 0$, то $x=2$. При этом $y=2$. Точка $(2, 2)$.<br>- При $x < 0$: $6 - x^2 = 4 + x \implies x^2 + x - 2 = 0 \implies (x+2)(x-1)=0$. Так как $x < 0$, то $x=-2$. При этом $y=2$. Точка $(-2, 2)$.<br>Ответ: Искомая фигура — это область, ограниченная сверху дугой параболы $y = 6 - x^2$ и снизу ломаной $y = 4 - |x|$, концами которой являются точки пересечения $(-2, 2)$ и $(2, 2)$.</p><p><strong>в)</strong></p><p>Рассмотрим систему неравенств $\begin{cases} 3x - y \ge 0 \\ x^2 + |y| \ge 4 \end{cases}$.<br>Перепишем систему: $\begin{cases} y \le 3x \\ |y| \ge 4 - x^2 \end{cases}$.<br>Первое неравенство, $y \le 3x$, задает полуплоскость, расположенную ниже и на прямой $y = 3x$, проходящей через начало координат.<br>Второе неравенство, $x^2 + |y| \ge 4$, задает область вне фигуры, ограниченной кривой $x^2 + |y| = 4$. Раскроем модуль:<br>- При $y \ge 0$: $x^2 + y \ge 4 \implies y \ge 4 - x^2$. Это область на и выше параболы $y = 4-x^2$.<br>- При $y < 0$: $x^2 - y \ge 4 \implies y \le x^2 - 4$. Это область на и ниже параболы $y = x^2-4$.<br>Таким образом, второе неравенство описывает всю плоскость, за исключением "глазоподобной" области между параболами $y=4-x^2$ и $y=x^2-4$.<br>Искомая фигура — это пересечение полуплоскости $y \le 3x$ и области, заданной вторым неравенством.<br>Ответ: Искомая фигура — это часть полуплоскости, лежащая на или ниже прямой $y = 3x$, из которой исключена открытая область, ограниченная кривой $x^2 + |y| = 4$.</p><p><strong>г)</strong></p><p>Рассмотрим систему неравенств $\begin{cases} x^2 + (y-1)^2 \le 16 \\ |y| + 3x \le 3 \end{cases}$.<br>Первое неравенство, $x^2 + (y-1)^2 \le 16$, задает круг с центром в точке $(0, 1)$ и радиусом $R=4$, включая его границу.<br>Второе неравенство, $|y| + 3x \le 3$, или $3x \le 3 - |y|$, задает область, ограниченную справа. Раскроем модуль:<br>- При $y \ge 0$: $y + 3x \le 3 \implies y \le 3 - 3x$. Это полуплоскость ниже и на прямой $y = 3-3x$.<br>- При $y < 0$: $-y + 3x \le 3 \implies y \ge 3x - 3$. Это полуплоскость выше и на прямой $y = 3x-3$.<br>Граница $y = 3-3x$ (для $y \ge 0$) и $y=3x-3$ (для $y < 0$) образует "уголок", открывающийся влево, с вершиной в точке $(1, 0)$. Неравенство задает область внутри этого "уголка" (то есть левее его границы).<br>Искомая фигура — это пересечение круга и области, заданной вторым неравенством.<br>Ответ: Искомая фигура — это часть круга с центром в $(0, 1)$ и радиусом 4, которая находится левее или на ломаной, состоящей из лучей $y = 3 - 3x$ для $y \ge 0$ и $y = 3x - 3$ для $y < 0$.</p>" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1107863" "type" => "task" ] "previous" => array:2 [ "refs" => "1107861" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1090 #items: array:1 [ 0 => App\Models\Book {#1114} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1070 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№163 (с. 52)
Условие. №163 (с. 52)
скриншот условия
163. Постройте в координатной плоскости фигуру, координаты каждой точки которой являются решениями системы неравенств:
a) $\begin{cases} x^2 + y^2 \le 16, \\ y \ge \frac{2}{x}, \end{cases}$
б) $\begin{cases} x^2 + y \le 6, \\ |x| + y \ge 4; \end{cases}$
в) $\begin{cases} 3x - y \ge 0, \\ x^2 + |y| \ge 4; \end{cases}$
г) $\begin{cases} x^2 + (y - 1)^2 \le 16, \\ |y| + 3x \le 3. \end{cases}$
Решение. №163 (с. 52)
Решение 2 (rus). №163 (с. 52)
a)
Рассмотрим систему неравенств $\begin{cases} x^2 + y^2 \le 16 \\ y \ge \frac{2}{x} \end{cases}$.
Первое неравенство, $x^2 + y^2 \le 16$, задает круг с центром в начале координат $(0, 0)$ и радиусом $R=4$, включая его границу.
Второе неравенство, $y \ge \frac{2}{x}$, задает множество точек, лежащих на и выше гиперболы $y = \frac{2}{x}$. Область определения этого неравенства — все $x$, кроме $x=0$. Гипербола имеет две ветви: одну в первой координатной четверти (при $x>0$) и одну в третьей (при $x<0$).
Искомая фигура является пересечением этих двух множеств. Это точки круга, которые одновременно удовлетворяют условию $y \ge \frac{2}{x}$. Фигура состоит из двух отдельных частей.
Ответ: Искомая фигура — это множество точек круга $x^2+y^2 \le 16$, которые находятся на или выше графика гиперболы $y = 2/x$. Фигура состоит из двух непересекающихся частей.
б)
Рассмотрим систему неравенств $\begin{cases} x^2 + y \le 6 \\ |x| + y \ge 4 \end{cases}$.
Перепишем систему в более удобном для построения виде: $\begin{cases} y \le 6 - x^2 \\ y \ge 4 - |x| \end{cases}$.
Первое неравенство, $y \le 6 - x^2$, задает область, расположенную ниже и на параболе $y = 6 - x^2$. Это парабола с ветвями, направленными вниз, и вершиной в точке $(0, 6)$.
Второе неравенство, $y \ge 4 - |x|$, задает область выше и на графике функции $y = 4 - |x|$. График $y = 4 - |x|$ представляет собой "уголок" с вершиной в точке $(0, 4)$ и ветвями, направленными вниз (прямые $y=4-x$ для $x \ge 0$ и $y=4+x$ для $x < 0$).
Искомая фигура — это область, заключенная между графиками этих двух функций. Найдем точки их пересечения, решив уравнение $6 - x^2 = 4 - |x|$.
- При $x \ge 0$: $6 - x^2 = 4 - x \implies x^2 - x - 2 = 0 \implies (x-2)(x+1)=0$. Так как $x \ge 0$, то $x=2$. При этом $y=2$. Точка $(2, 2)$.
- При $x < 0$: $6 - x^2 = 4 + x \implies x^2 + x - 2 = 0 \implies (x+2)(x-1)=0$. Так как $x < 0$, то $x=-2$. При этом $y=2$. Точка $(-2, 2)$.
Ответ: Искомая фигура — это область, ограниченная сверху дугой параболы $y = 6 - x^2$ и снизу ломаной $y = 4 - |x|$, концами которой являются точки пересечения $(-2, 2)$ и $(2, 2)$.
в)
Рассмотрим систему неравенств $\begin{cases} 3x - y \ge 0 \\ x^2 + |y| \ge 4 \end{cases}$.
Перепишем систему: $\begin{cases} y \le 3x \\ |y| \ge 4 - x^2 \end{cases}$.
Первое неравенство, $y \le 3x$, задает полуплоскость, расположенную ниже и на прямой $y = 3x$, проходящей через начало координат.
Второе неравенство, $x^2 + |y| \ge 4$, задает область вне фигуры, ограниченной кривой $x^2 + |y| = 4$. Раскроем модуль:
- При $y \ge 0$: $x^2 + y \ge 4 \implies y \ge 4 - x^2$. Это область на и выше параболы $y = 4-x^2$.
- При $y < 0$: $x^2 - y \ge 4 \implies y \le x^2 - 4$. Это область на и ниже параболы $y = x^2-4$.
Таким образом, второе неравенство описывает всю плоскость, за исключением "глазоподобной" области между параболами $y=4-x^2$ и $y=x^2-4$.
Искомая фигура — это пересечение полуплоскости $y \le 3x$ и области, заданной вторым неравенством.
Ответ: Искомая фигура — это часть полуплоскости, лежащая на или ниже прямой $y = 3x$, из которой исключена открытая область, ограниченная кривой $x^2 + |y| = 4$.
г)
Рассмотрим систему неравенств $\begin{cases} x^2 + (y-1)^2 \le 16 \\ |y| + 3x \le 3 \end{cases}$.
Первое неравенство, $x^2 + (y-1)^2 \le 16$, задает круг с центром в точке $(0, 1)$ и радиусом $R=4$, включая его границу.
Второе неравенство, $|y| + 3x \le 3$, или $3x \le 3 - |y|$, задает область, ограниченную справа. Раскроем модуль:
- При $y \ge 0$: $y + 3x \le 3 \implies y \le 3 - 3x$. Это полуплоскость ниже и на прямой $y = 3-3x$.
- При $y < 0$: $-y + 3x \le 3 \implies y \ge 3x - 3$. Это полуплоскость выше и на прямой $y = 3x-3$.
Граница $y = 3-3x$ (для $y \ge 0$) и $y=3x-3$ (для $y < 0$) образует "уголок", открывающийся влево, с вершиной в точке $(1, 0)$. Неравенство задает область внутри этого "уголка" (то есть левее его границы).
Искомая фигура — это пересечение круга и области, заданной вторым неравенством.
Ответ: Искомая фигура — это часть круга с центром в $(0, 1)$ и радиусом 4, которая находится левее или на ломаной, состоящей из лучей $y = 3 - 3x$ для $y \ge 0$ и $y = 3x - 3$ для $y < 0$.
Другие задания:
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